Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1800b
if this polytope has a name.
Group : SmallGroup(1800,575)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 150, 450, 30
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,6}*600a
   6-fold quotients : {10,6}*300
   25-fold quotients : {6,6}*72b
   50-fold quotients : {6,3}*36
   75-fold quotients : {2,6}*24
   150-fold quotients : {2,3}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)(34,73)
(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)(45,62)
(46,56)(47,60)(48,59)(49,58)(50,57);;
s1 := ( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,33)( 7,32)( 8,31)( 9,35)(10,34)
(11,39)(12,38)(13,37)(14,36)(15,40)(16,45)(17,44)(18,43)(19,42)(20,41)(21,46)
(22,50)(23,49)(24,48)(25,47)(51,52)(53,55)(56,58)(59,60)(61,64)(62,63)(66,70)
(67,69)(72,75)(73,74);;
s2 := ( 2,25)( 3,19)( 4,13)( 5, 7)( 8,24)( 9,18)(10,12)(14,23)(15,17)(20,22)
(26,51)(27,75)(28,69)(29,63)(30,57)(31,56)(32,55)(33,74)(34,68)(35,62)(36,61)
(37,60)(38,54)(39,73)(40,67)(41,66)(42,65)(43,59)(44,53)(45,72)(46,71)(47,70)
(48,64)(49,58)(50,52);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)
(13,19)(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)
(34,73)(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)
(45,62)(46,56)(47,60)(48,59)(49,58)(50,57);
s1 := Sym(75)!( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,33)( 7,32)( 8,31)( 9,35)
(10,34)(11,39)(12,38)(13,37)(14,36)(15,40)(16,45)(17,44)(18,43)(19,42)(20,41)
(21,46)(22,50)(23,49)(24,48)(25,47)(51,52)(53,55)(56,58)(59,60)(61,64)(62,63)
(66,70)(67,69)(72,75)(73,74);
s2 := Sym(75)!( 2,25)( 3,19)( 4,13)( 5, 7)( 8,24)( 9,18)(10,12)(14,23)(15,17)
(20,22)(26,51)(27,75)(28,69)(29,63)(30,57)(31,56)(32,55)(33,74)(34,68)(35,62)
(36,61)(37,60)(38,54)(39,73)(40,67)(41,66)(42,65)(43,59)(44,53)(45,72)(46,71)
(47,70)(48,64)(49,58)(50,52);
poly := sub<Sym(75)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope